4 An Introduction to Emergence Dynamics in Complex Systems
161
It should be stressed that there exist many fundamental topologies on a large
network that may induce various possible sustained oscillations. Competitions and
collaborations among these sub-networks and rhythms lead to complicated dynamics.
4.4 Synchronization: Cooperations of Rhythms
4.4.1 Synchrony: An Overview
Collective behavior of complex and nonlinear systems has a variety of specific manifestations, and synchronization should be one of the most fundamental phenomena
[76, 77]. Discussions of fundamental problems in synchronization cover a variety of
fields of natural science and engineering, and even many behaviors in social science
are closely related to the basic feature of synchronization. Many specific systems
such as pendula, musical instruments, electronic devices, lasers, biological systems,
neurons, cardiology and so on, exhibit very rich synchronous phenomena.
Let us first focus on fireflies, a magical insect on earth. A male firefly can
release a special luminescent substance to produce switched periodic flashes to attract
females. This corresponds to a typical biological sustained oscillation. A surprising
phenomenon occurs when a large number of male fireflies gather together in the dark
of night to produce synchronized flashings. This phenomenon was first written in the
log of the naturalist and traveler, Engeekert Kaempfer in 1680 when he traveled in
Thailand. Later in 1935, Hugh Smith reported his observation on the synchronized
flashing of fireflies [78]. More explorations have been performed after these initial
observations. Interestingly, Buck elaborated on this phenomenon and published two
articles with the same title “synchronized flashing of fireflies” on the same journal
in 1938 and 1988, respectively [79].
It is a complex issue in biology to explore the implication of the synchronization
flashing of male fireflies. The physical mechanism behind this phenomenon may be
more important and interesting because it is a typical dynamical process. If each
firefly is considered as an oscillator, the synchronous flashing is an emergent order
produced by these oscillators. This collective behavior is obviously originated from
the interaction between individuals, and the interplay between them results in an
adjustment of the rhythm of every firefly.
Accidentally and interestingly, before Kempfer’s finding of firefly synchronization, Huygens described the synchronization of two coupled pendula [80] in 1673. He
discovered that a couple of pendulum clocks hanging from a common support
had synchronized, i.e. their oscillations coincided perfectly and the pendula moved
always in opposite directions. He also proposed his understanding of the phenomenon
by attributing to the coupling brought by the beam that hang two pendula and the
coupling-induced energy transfer between the two pendulum clocks.
161
It should be stressed that there exist many fundamental topologies on a large
network that may induce various possible sustained oscillations. Competitions and
collaborations among these sub-networks and rhythms lead to complicated dynamics.
4.4 Synchronization: Cooperations of Rhythms
4.4.1 Synchrony: An Overview
Collective behavior of complex and nonlinear systems has a variety of specific manifestations, and synchronization should be one of the most fundamental phenomena
[76, 77]. Discussions of fundamental problems in synchronization cover a variety of
fields of natural science and engineering, and even many behaviors in social science
are closely related to the basic feature of synchronization. Many specific systems
such as pendula, musical instruments, electronic devices, lasers, biological systems,
neurons, cardiology and so on, exhibit very rich synchronous phenomena.
Let us first focus on fireflies, a magical insect on earth. A male firefly can
release a special luminescent substance to produce switched periodic flashes to attract
females. This corresponds to a typical biological sustained oscillation. A surprising
phenomenon occurs when a large number of male fireflies gather together in the dark
of night to produce synchronized flashings. This phenomenon was first written in the
log of the naturalist and traveler, Engeekert Kaempfer in 1680 when he traveled in
Thailand. Later in 1935, Hugh Smith reported his observation on the synchronized
flashing of fireflies [78]. More explorations have been performed after these initial
observations. Interestingly, Buck elaborated on this phenomenon and published two
articles with the same title “synchronized flashing of fireflies” on the same journal
in 1938 and 1988, respectively [79].
It is a complex issue in biology to explore the implication of the synchronization
flashing of male fireflies. The physical mechanism behind this phenomenon may be
more important and interesting because it is a typical dynamical process. If each
firefly is considered as an oscillator, the synchronous flashing is an emergent order
produced by these oscillators. This collective behavior is obviously originated from
the interaction between individuals, and the interplay between them results in an
adjustment of the rhythm of every firefly.
Accidentally and interestingly, before Kempfer’s finding of firefly synchronization, Huygens described the synchronization of two coupled pendula [80] in 1673. He
discovered that a couple of pendulum clocks hanging from a common support
had synchronized, i.e. their oscillations coincided perfectly and the pendula moved
always in opposite directions. He also proposed his understanding of the phenomenon
by attributing to the coupling brought by the beam that hang two pendula and the
coupling-induced energy transfer between the two pendulum clocks.